NO FULL TEXT AVAILABLE. This thesis contains 3rd party copyright material. ----- A bifurcation theory is applied to multimachine power system to investigate the
complex dynamics of the system. The second system of the IEEE second benchmark
model of Subsynchronous Resonance (SSR) is considered. The system can be
mathematically modeled as a set of first order nonlinear ordinary differential
equations with the compensation factor (μ=X/XL) as a bifurcation (control)
parameter. So, bifurcation theory can be applied to nonlinear dynamical systems,
which can be written as dxldt = F(x,·μ).
The contribution of this research is to apply the bifurcation theory and chaos to the
considered power system. Initially, the system is modeled as a set of first order
nonlinear ordinary differential equations with the compensation factor as a
bifurcation parameter. The effect of machine components, i.e. damper winding,
Automatic Voltage Regulator (A VR), and Power System Stabilizer (PSS), and
machine saturation are considered. Linear and nonlinear controllers are used to
control the Hopf bifurcation and chaos utilizing bifurcation theory and center
manifold theory. Furthermore, Flexible AC Transmission System (FACTS)
controllers are used to control bifurcations of subsynchronous resonance in the
considered power system.
First of all, the case of neglecting the dynamics of damper windings, Automatic
Voltage Regulator (A VR) and Power System Stabilizer (PSS) is considered. The
results show that as the compensation factor (~t) increases, the operating point loses
stability via Hopf bifurcation point (H) and a limit cycle is born at μ=H. This limit
cycle is stable if the bifurcation is supercritical and unstable if it is subcritical. As μ
increases further, the limit cycle grows and then loses stability through secondary
Hopf bifurcation. Hence, a period quasiperiodic attractor appears. Also, as μ
increases further, a chaotic solution is obtained. However, this solution is bounded.
The effects of machine components, i.e. damper winding, A VR, and PSS on
subsynchronous resonance in a power system are studied. The results show that
these components affect the locations, number and type of the Hopf bifurcations.
The influences of adding damper windings along the d- and q-axes to the generator
are investigated. In this case, there was a certain effect on the Hopf bifurcation
which involves location, number and type. The effect of q-axis damper winding is
much more destabilizing than that of the d-axis damper winding. Another studied
case is the use of A VR together with PSS. This resulted in qualitative and
quantitative changes in Hopf bifurcation. Moreover, the influence of iron saturation
on the complex dynamics of the system is studied. The results show that the
influence of machine saturation expands the unstable region when the system loses
stability at the Hopf bifurcation point at a less value of compensation.
Based on bifurcation theory and center manifold theory, both linear and nonlinear
controllers are used to control the Hopf bifurcation and chaos. The results show that
linear controller can only delay the inception of a bifurcation to some desired value
of the bifurcation parameter. In linear controller the critical modes must be
controllable. When the control objective is set to stabilize the periodic solution,
nonlinear controller must be used.
Flexible AC Transmission System (FACTS) controllers are used to control
bifurcations of Subsynchronous Resonance (SSR) in the considered power system.
To avoid SSR in the power system, the use of FACTS devices such as the Thyristor
Controlled Series Capacitor (TCSC), the Static Synchronous Series Compensator
(SSSC) and the Static Compensator (ST A TCOM) are propo ed. When FACTS
controlJers are considered, the response of the system shows that FACTS stabilize
the system by eliminating the bifurcations at which subsynchronous resonance
occur. Therefore, the system never loses stability for all values of the compensation